Module: Standard C++ Library Library: Numerics
Function
Generalized numeric operation that calculates successive partial sums of a range of values
#include <numeric>
namespace std {
template <class InputIterator, class OutputIterator>
OutputIterator partial_sum(InputIterator start,
InputIterator finish,
OutputIterator result);
template <class InputIterator,
class OutputIterator,
class BinaryOperation>
OutputIterator partial_sum(InputIterator start,
InputIterator finish,
OutputIterator result,
BinaryOperation binary_op);
}
The partial_sum() algorithm creates a new sequence in which every element is formed by adding all the values of the previous elements, or, in the second form of the algorithm, by applying the operation binary_op successively on every previous element. That is, partial_sum() assigns to every iterator i in the range [result, result + (finish - start)) a value equal to:
((...(*start + *(start + 1)) + ... ) +
*(start + (i - result)))
or, in the second version of the algorithm:
binary_op(binary_op(..., binary_op (*start,
*(start + 1)),...),*(start + (i - result)))
For instance, applying partial_sum() to (1,2,3,4,) yields (1,3,6,10).
The partial_sum() algorithm returns result + (finish - start).
If result is equal to start, the elements of the new sequence successively replace the elements in the original sequence, effectively turning partial_sum() into an inplace transformation.
Exactly (finish - start) - 1 applications of the default + operator or binary_op are performed.
//
// partsum.cpp
//
#include <algorithm> // for copy
#include <functional> // for multiplies
#include <iostream> // for cout, endl
#include <iterator> // for ostream_iterator
#include <numeric> // for partial_sum
#include <vector> // for vector
int main ()
{
typedef std::vector<int, std::allocator<int> > Vector;
typedef std::ostream_iterator<int, char,
std::char_traits<char> >
Iter;
// Initialize a vector using an array of integers.
const Vector::value_type a[] = { 1, 2, 3, 4, 5,
6, 7, 8, 9, 10 };
Vector v (a + 0, a + sizeof a / sizeof *a);
// Create an empty vectors to store results.
Vector sums (Vector::size_type (10));
Vector prods (Vector::size_type (10));
// Compute partial_sums and partial_products.
std::partial_sum (v.begin (), v.end (), sums.begin ());
std::partial_sum (v.begin (), v.end (), prods.begin (),
std::multiplies<Vector::value_type>());
// Output the results.
std::cout << "For the series: \n ";
std::copy (v.begin (), v.end (), Iter (std::cout, " "));
std::cout << "\n\nThe partial sums: \n ";
std::copy (sums.begin (), sums.end (), Iter (std::cout,
" "));
std::cout << " should each equal (N*N + N)/2\n\n";
std::cout << "The partial products: \n ";
std::copy (prods.begin (), prods.end (), Iter (std::cout,
" "));
std::cout << " should each equal N!" << std::endl;
return 0;
}
Program Output:
For the series:
1 2 3 4 5 6 7 8 9 10
The partial sums:
1 3 6 10 15 21 28 36 45 55 should each equal (N*N + N)/2
The partial products:
1 2 6 24 120 720 5040 40320 362880 3628800 should each
equal N!
ISO/IEC 14882:1998 -- International Standard for Information Systems -- Programming Language C++, Section 26.4.3
Copyright (c) 1994-2006 Rogue Wave Software, a Quovadx Division.
Licensed under the Apache License, Version 2.0.
Contact Rogue Wave about documentation or support issues. You can also seek help from other developers through the Apache stdcxx community (see below).